Staal has a three-game goal streak for the Hurricanes, who have won three straight and five of their past six Stanley Cup Playoff games. They eliminated the Washington Capitals in a double-overtime Game 7 of the first round Wednesday.
"I'm just trying to get goals and trying to win games," Staal said. "I'm not really sure (where the scoring is coming from), but I can't complain. We came into this game feeling good about ourselves, knowing our game is rising. We need to stay with it and hopefully things will continue to go our way."
Game 2 of the best-of-7 series is at New York on Sunday.
"They just play all-out, they don't give up," Lee said. "They played a good, hard hockey game. They were really good on the penalty kill and their defense stood us up really well entering the zone and made it difficult on us getting set up."
It was Mrazek's second shutout of the playoffs and fifth in 19 NHL postseason games.
"These are the games where one bad bounce could change anything, and I think that was the type of game we played tonight," Mrazek said. "We're happy with taking Game 1, but now we have to prepare for Game 2."